Equilibrium-diffusion limit of the radiation model

2025/04/25 by Lei Li, Li, Lei
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Radiative Heat Transfer Studies

paper · pdf · doi:10.48550/arxiv.2504.18094

openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We justify rigorously the equilibrium-diffusion limit of the model consists of a radiative transfer satisfied by the specific intensity of radiation coupled to a diffusion equation satisfied by the material temperature. For general initial data, we construct the existence of the solution to the coupled model in \mathbbT³ by the Hilbert expansion and prove the convergence of the solutions to the limiting system in the equilibrium-diffusion regime. Moreover, the initial layer for the radiative density and the temperature are constructed to get the strong convergence in L^∞ norm. We also get the convergence rates about the intensity of radiation and temperature in this paper.

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